Theorem funALTVeqd 38698

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 38696	. 2 ⊢ (𝐴 = 𝐵 → ( FunALTV 𝐴 ↔ FunALTV 𝐵))
3	1, 2	syl 17	1 ⊢ (𝜑 → ( FunALTV 𝐴 ↔ FunALTV 𝐵))

Syntax hints:   → wi 4   ↔ wb 206   = wceq 1539   FunALTV wfunALTV 38207

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708  ax-sep 5305  ax-nul 5315  ax-pr 5441

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1542  df-fal 1552  df-ex 1779  df-nf 1783  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3483  df-dif 3969  df-un 3971  df-in 3973  df-ss 3983  df-nul 4343  df-if 4535  df-sn 4635  df-pr 4637  df-op 4641  df-br 5152  df-opab 5214  df-id 5587  df-xp 5699  df-rel 5700  df-cnv 5701  df-co 5702  df-dm 5703  df-rn 5704  df-res 5705  df-coss 38407  df-cnvrefrel 38523  df-funALTV 38678

This theorem is referenced by: (None)