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Mirrors > Home > NFE Home > Th. List > eqidd | GIF version |
Description: Class identity law with antecedent. (Contributed by NM, 21-Aug-2008.) |
Ref | Expression |
---|---|
eqidd | ⊢ (φ → A = A) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2353 | . 2 ⊢ A = A | |
2 | 1 | a1i 10 | 1 ⊢ (φ → A = A) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1642 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-cleq 2346 |
This theorem is referenced by: nfabd2 2507 cbvraldva 2841 cbvrexdva 2842 iotanul 4354 fvopab4t 5385 eqfnov2 5590 mpteq1 5658 cbvmpt2 5679 erthi 5970 spaccl 6286 |
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