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Mirrors > Home > MPE Home > Th. List > Mathboxes > axc5sp1 | Structured version Visualization version GIF version |
Description: A special case of ax-c5 33186 without using ax-c5 33186 or ax-5 1827. (Contributed by NM, 13-Jan-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
axc5sp1 | ⊢ (∀𝑦 ¬ 𝑥 = 𝑥 → ¬ 𝑥 = 𝑥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equidqe 33225 | . 2 ⊢ ¬ ∀𝑦 ¬ 𝑥 = 𝑥 | |
2 | 1 | pm2.21i 115 | 1 ⊢ (∀𝑦 ¬ 𝑥 = 𝑥 → ¬ 𝑥 = 𝑥) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1473 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-c7 33188 ax-c10 33189 |
This theorem depends on definitions: df-bi 196 df-an 385 df-ex 1696 |
This theorem is referenced by: (None) |
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