Theorem funALTVeqd 39382

Description: Equality deduction for the function predicate. (Contributed by NM, 23-Feb-2013.)

Hypothesis

Ref	Expression
funALTVeqd.1	⊢ (𝜑 → 𝐴 = 𝐵)

Assertion

Ref	Expression
funALTVeqd	⊢ (𝜑 → ( FunALTV 𝐴 ↔ FunALTV 𝐵))

Proof of Theorem funALTVeqd

Step	Hyp	Ref	Expression
1		funALTVeqd.1	. 2 ⊢ (𝜑 → 𝐴 = 𝐵)
2		funALTVeq 39380	. 2 ⊢ (𝐴 = 𝐵 → ( FunALTV 𝐴 ↔ FunALTV 𝐵))
3	1, 2	syl 18	1 ⊢ (𝜑 → ( FunALTV 𝐴 ↔ FunALTV 𝐵))

Syntax hints:   → wi 4   ↔ wb 209   = wceq 1568   FunALTV wfunALTV 38811

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2143  ax-9 2151  ax-11 2190  ax-ext 2733  ax-sep 5256  ax-pr 5404

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1103  df-tru 1571  df-fal 1581  df-ex 1808  df-sb 2095  df-clab 2740  df-cleq 2753  df-clel 2836  df-ral 3078  df-rex 3088  df-rab 3415  df-v 3455  df-dif 3907  df-un 3909  df-in 3911  df-ss 3921  df-nul 4286  df-if 4487  df-sn 4589  df-pr 4591  df-op 4595  df-br 5109  df-opab 5173  df-id 5556  df-xp 5667  df-rel 5668  df-cnv 5669  df-co 5670  df-dm 5671  df-rn 5672  df-res 5673  df-coss 39096  df-cnvrefrel 39202  df-funALTV 39362

This theorem is referenced by: (None)