Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > con4iOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of con4i 113 as of 15-Jul-2021. This shorter proof has been reverted to its original to avoid a dependency on ax-1 6 and ax-2 7. (Contributed by NM, 29-Dec-1992.) (Proof shortened by Wolf Lammen, 21-Jun-2013.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
con4iOLD.1 | ⊢ (¬ 𝜑 → ¬ 𝜓) |
Ref | Expression |
---|---|
con4iOLD | ⊢ (𝜓 → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnot 136 | . 2 ⊢ (𝜓 → ¬ ¬ 𝜓) | |
2 | con4iOLD.1 | . 2 ⊢ (¬ 𝜑 → ¬ 𝜓) | |
3 | 1, 2 | nsyl2 142 | 1 ⊢ (𝜓 → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |