Theorem axfrege52c 44671

Description: Justification for ax-frege52c 44672. (Contributed by RP, 24-Dec-2019.)

Assertion

Ref	Expression
axfrege52c	⊢ (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 → [𝐵 / 𝑥]𝜑))

Proof of Theorem axfrege52c

Step	Hyp	Ref	Expression
1		dfsbcq 3748	. 2 ⊢ (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 ↔ [𝐵 / 𝑥]𝜑))
2	1	biimpd 232	1 ⊢ (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 → [𝐵 / 𝑥]𝜑))

This proof depends on syntax axioms:   → wi 4   = wceq 1570  [wsbc 3746

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-cleq 2757  df-clel 2840  df-sbc 3747

This theorem is used by: (None)